1. Field of the Invention
The present invention relates to a wave speed meter for determining the propagation speed of a shear induced wave in a viscoelastic fluid.
2. Description of the Prior Art
Viscoelastic fluids such as polymer solutions and melts of polymers (molten plastic), can support the propagation of various kinds of waves of shear; in such fluids an event which takes place in one place in the fluid will take a certain time to reach another place. These wave speeds are a fundamental property of elastic fluids, but no instruments exist for directly measuring the wave speeds.
The propagation of shear induced waves through viscoelastic fluids has been discussed in a thesis prepared by Eugene Bach Lieb, at the University of Rochester, Rochester, N.Y., 1975, entitled "Viscoelastic Flow Behavior In Accelerating Shear Fields." Measurement of wave speed was made utilizing photographic techniques which illustrated traveling shear waves across a gap in a rheometer.
In an article entitled "Linearized Dynamics For Step Jumps Of Velocity In Displacement Of Shearing Flows Of A Simple Fluid," Rheologica Acta, 21, pp. 228-250, 1982, A . Narain and D. D. Joseph (one of the present inventors) showed that the propagation speed of small amplitude waves of slip lines of velocity and displacement is given by ##EQU1## where .rho. is the density of the fluid and G(0) is the instantaneous value of the shear relaxation modulus of the fluid or liquid that is being tested. There are some methods currently available to measure the relaxation function G(s) of some liquids, but these methods are not accurate for small values of the lapsed time s. By measuring the wave speed "C", the instantaneous value G(0) of the relaxation function G(s) can be determined.
An additional reference to descriptions of the relaxation function G(s) includes the article entitled "Remarks About The Interpretation Of Impulse Experiments In Shear Flows Of Viscoelastic Liquids," A. Narain and D. D. Joseph, Rheologica Acta, 22, pp. 528-538, 1983.